Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON):

Solution:
import math
# -*- coding: utf-8 -*-

#$BF~NO$7$?$b$N$rBeF~(B
input_num = int(raw_input())
twi_num = input_num * 2

ans = "NO"
for i in range(1, int(math.sqrt(input_num+1))+1):
	if(ans == "YES"):
		break;

	temp = twi_num - (i * (i+1))

	for j in range(-1, 2):
		check = int(math.sqrt(temp)) + j
		if(check < 0):
			break;
		if((check * (check+1)) + (i * (i+1))== twi_num):
			ans = "YES"

print ans